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International Journal of Naval Architecture and Ocean Engineering xx (2016) 1e11http://www.journals.elsevier.com/international-journal-of-naval-architecture-and-ocean-engineering/

Numerical study of ship motions and added resistance in regular incidentwaves of KVLCC2 model

Yavuz Hakan Ozdemir a,1, Baris Barlas b,*a Bartin University, Vocational School, Bartin, Turkey

b Istanbul Technical University, Faculty of Naval Arch & Ocean Engineering, Istanbul, Turkey

Received 20 June 2016; revised 1 September 2016; accepted 4 September 2016

Available online ▪ ▪ ▪

Abstract

In this study, the numerical investigation of ship motions and added resistance at constant forward velocity of KVLCC2 model is presented.Finite volume CFD code is used to calculate three dimensional, incompressible, unsteady RANS equations. Numerical computations show thatreliable numerical results can be obtained in head waves. In the numerical analyses, body attached mesh method is used to simulate the shipmotions. Free surface is simulated by using VOF method. The relationship between the turbulence viscosity and the velocities are obtainedthrough the standard k � ε turbulence model. The numerical results are examined in terms of ship resistance, ship motions and added resistance.The validation studies are carried out by comparing the present results obtained for the KVLCC2 hull from the literature. It is shown that, shipresistance, pitch and heave motions in regular head waves can be estimated accurately, although, added resistance can be predicted with someerror.Copyright © 2016 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under theCC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Ship motions; RANSE; Turbulent free surface flows; Added wave resistance

1. Introduction

The use of numerical models for predicting the ship per-formance in preliminary design step is getting in common. Themodel experiments are still very valuable; hence, time and costencourage the use of Computational Fluid Dynamics (CFD).In the past, CFD approaches were based on potential flowtheory because the NaviereStokes equation was difficult tosolve. There are some approaches in solving NaviereStokesequations, but recent developments in computing technologyenable researchers to solve the problems in shipbuilding

* Corresponding author. Fax: þ90 212 2856454.

E-mail addresses: [email protected] (Y.H. Ozdemir), barlas@itu.

edu.tr (B. Barlas).

Peer review under responsibility of Society of Naval Architects of Korea.1 Fax: þ90 378 2278875.

Please cite this article in press as: Ozdemir, Y.H., Barlas, B., Numerical study of sh

International Journal of Naval Architecture and Ocean Engineering (2016), http:/

http://dx.doi.org/10.1016/j.ijnaoe.2016.09.001

2092-6782/Copyright © 2016 Society of Naval Architects of Korea. Production and h

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

industry by means of Reynolds-Averaged NaviereStokes(RANS) equations.

The prediction of added resistance of a ship in waves isimportant for the ship's performance and seakeeping. Somemethods can be found in the literature, but the most reliableones are based on the linear strip theory of Salvesen et al.(1970). Many studies practiced potential flow methods usedin hydrodynamics (Salvesen, 1978; Faltinsen et al., 1980).Recently, RANS methods gain advantage. Several researchershave studied the motions and added resistance of a ship. Someof these studies were based on potential theory, others werebased on RANS. Furthermore, most of the work done wasrestricted to regular head waves. Fang (1998) developed arobust method to calculate the added resistance of SWATHships advancing in regular waves. Modeling of free surfaceflows around different test cases have been reported by Satoet al. (1999), by using RANS equation. The well-knownstrip theory was still used in his method. Orihara and Miyata

ip motions and added resistance in regular incident waves of KVLCC2 model,

/dx.doi.org/10.1016/j.ijnaoe.2016.09.001

osting by Elsevier B.V. This is an open access article under the CC BY-NC-ND

http://creativecommons.org/licenses/by-nc-nd/4.0/

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2 Y.H. Ozdemir, B. Barlas / International Journal of Naval Architecture and Ocean Engineering xx (2016) 1e11

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(2003) developed a CFD method using RANS equations toestimate the added resistance of ships in waves. Some methodsthat can be used to predict the added resistance of a monohullship were investigated and validated by means of the experi-mental study of Arribas (2007). Wilson et al. (2006), simulatedroll decay motion by using unsteady RANS equation. A flow-simulation method was developed to predict the performanceof a high-speed vessel in unsteady motion on a free surface byPanahani et al. (2009). The ship motion conditions of the high-speed vessel are virtually realized by combining the simula-tions of water-flow and the motion of the vessel. Deng et al.(2010) use a RANS solver using Finite Volume (FV) dis-cretization and free surface capturing approach. In this study,it was shown that special attention required for time dis-cretization. Matulja et al. (2011) estimated the added resis-tance of four different merchant ships by using three differentmethods and compare them with the experiments. The addedresistance of KVLCC2 in small amplitude short and regularwaves (1.090 � L/l � 5.526) were investigated using striptheory and experimentally by Guo and Steen (2011). Liu et al.(2011) estimated the added resistance of ships using a 3Dpanel, and time-domain Rankine source-Green functionmethods, and validated the applicability of the implementedmethods by using wide range of hull forms. Guo et al. (2012)presented to the prediction of added resistance and ship mo-tion of KVLCC2 model in head waves by using RANSequation. The motions and added resistance of KVLCC2 attwo different Froude numbers with free and fixed surge inshort (2.091 � L/l � 5.525) and long (1.67 � L/l � 0.5) headwaves were predicted using URANS by Sadat-Hosseini et al.(2013) and verifications showed that the results were fairlyinsensitive to the grid size and the time step. Zhirong andDecheng (2013) investigated the added resistance, heave andpitch motions in head waves using RANS. Masashi (2013)investigated the effects of nonlinear ship-generated unsteadywaves, ship motions and added resistance by using blunt andslender Wigley forms. It was found that near the peak value ofadded resistance the degree of nonlinearity in the unsteadywave became noticeable. Seo et al. (2013) studied on thecomparison of the computation of added resistance and vali-dation with experimental data on Wigley and Series 60 hulls,and S175 container ship. They used three different methods;the Rankine panel, strip theory, and Cartesian grid.

In the present study, two different physical problems of theKVLCC2 container ship is examined: total ship resistancemodeled in calm water and the free heave and pitch motionresponse due to the incident waves. The KVLCC2 wasdesigned at the Korea Research Institute for Ships and OceanEngineering (now MOERI) around 1997 to be used as a testcase for CFD predictions. KVLCC2 was selected as a test casein the Gothenburg 2010 CFD workshop (G2010, 2010). Bothfree heave and pitch motion in head waves are performed. Theship resistances in waves are also analyzed. The added resis-tance is calculated by subtracting the steady surge force fromthe mean surge force calculated from the equations of motion.The present work is performed to show the capability ofgeneral purpose CFD code of Star CCM þ for design, analysis



and reliability, and to carry out validation analysis on a per-sonal computer. The finite volume solution method for theRANS equation is applied to the unsteady turbulent flowsimulation. The turbulence model used is the well-knownstandard k � ε two-equation turbulence model. The nextsection of this paper provides brief explanations about thegoverning equations, boundary conditions, computations,validation, and conclusions.

2. Geometry and conditions

As the KVLCC2 hull form is used for seakeeping and totalresistance simulations, the geometry of the KVLCC2 shipmodel is given in Fig. 1. G is the center of gravity, which is theorigin of a ship-fixed reference frame, it is set in the plane ofthe undisturbed free surface; the z axis is the vertical direction,positive upward, the x axis is in the aft direction, and y thelateral direction. In order to evaluate the numerical andexperimental results, a right-handed coordinate system is used(Panahani et al., 2009). The model hull does not have a rudderand a propeller. The KVLCC2 model has a scale of 1/58 that isimplemented for the numerical calculations. Table 1 gives themodel ship and main ship particulars.

Guo et al. (2012) have investigated sinkage and trim ofKVLCC2 container ship. They showed that sinkage and trimvalues of KVLCC2 are very small. For this reason in this studymodel fixed from its floating position and it is not free tosinkage and trim, their effects on ship resistance are neglected.During the ship motion analysis, the pitching and heavingmotions are free, and other motions are not permitted. Bothship motion and ship resistance simulation, the effect of thewind is not taken into account. Three different seakeepingsimulation conditions are given in Table 2. U is the ship speed,f is the wave frequency, fe is the encounter frequency, l is thewave length and z is the wave amplitude.

3. Mathematical formulation

3.1. Governing equations

The equation for the translation of the center of mass of theship body is given as;

mdv

dt¼ f ð1Þ

where m represents the mass of the body, f is the resultantforce acting on the body and v is the velocity of the center ofmass. An angular momentum equation of the body is formu-lated in the body local coordinate system with the origin in thecenter of the body;

Mdu

dtþu�Mu¼ n ð2Þ

where M is the tensor of moments of inertia, u is the angularvelocity of rigid body, and n is the resultant moment acting onthe body. The resulting force and moment acting on the ship



Fig. 1. KVLCC2 geometry for pitch and heave in head waves at constant forward speed.

Table 1

Geometrical properties of KVLCC2.

Symbol Ship Model

Scale l 1 58

Length between perpendiculars LPP (m) 320.0 5.5172

Maximum beam of waterline B (m) 58.0 1.0000

Draft T (m) 20.8 0.3586

Block coefficient CB 0.8098 0.8098

Displacement V (m3) 312,622 1.6023

Moment of inertia Kxx/B 0.40 0.40

Moment of inertia Kyy/LPP, Kzz/LPP 0.25/0.25 0.25/0.25

Froude number Fr 0.142 0.142

Speed U (m/s) 7.973 1.044

Table 2

Coupled pitch and heave simulation conditions.

Condition no. C1 C2 C3

Froude number (Fr) 0.142 0.142 0.142

Wave length l/LPP 0.9171 1.1662 1.600

Wave amplitude z (mm) 75 75 75

Wave frequency f (Hz) 0.555 0.492 0.420

Encounter frequency fe (Hz) 0.761 0.654 0.538

3Y.H. Ozdemir, B. Barlas / International Journal of Naval Architecture and Ocean Engineering xx (2016) 1e11

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are obtained from fluid pressure and shear force acting on theeach boundary face of the body. The translations of the shipare estimated according the computed velocity and pressurefields in the flow domain. A more detailed discussion of thispoint is provided in (Panahani et al., 2009).

The governing equations are the RANS equations and thecontinuity equation for mean velocity of the unsteady, three-dimensional incompressible flow. The continuity equationand momentum equations in Cartesian coordinates can begiven as:

vUi

vxj¼ 0 ð3Þ

for the continuity,

vUi

vtþ v

�UiUj

�vxj

¼�1

r

vP

vxiþ v

vxj

�n

�vUi

vxjþ vUj

vxi

� ��v�u0iu

0j

vxj

ð4Þ

for the momentum equations, where Ui and u0i express themean and fluctuation velocity component in the direction of



the Cartesian coordinate xi, p the mean pressure, r the densityand n the kinematic viscosity. The Reynolds stress tensor isthen calculated by using the well-known Boussinesq model:

u0iu0j ¼�nt

�vUi

vxjþ vUj

vxi

�þ 2

3dijk ð5Þ

The eddy viscosity nt is expressed as nt ¼ Cmk2=ε, where

Cm is an empirical constant ðCm ¼ 0:09Þ, k the turbulent ki-netic energy and ε the dissipation rate of k. The turbulencequantities k and ε are then computed from a k � ε model usingtwo transport equations. The well-known standard k � ε two-equation turbulence model has been used to simulate the tur-bulent flows. The turbulent kinetic energy, k, and the rate ofdissipation of the turbulent energy, ε are (Chau et al., 2005):

vk

vtþ v

�kUj

�vxj

¼ v

vxj

��nþ nt

sk

�vk

vxj

�þ Pk � ε ð6Þ

vε

vtþ v

�εUj

�vxj

¼ v

vxj

��nþ nt

sε

�vε

vxj

�þC

ε1Pk

ε

k�C

ε2

ε2

kð7Þ

Pk ¼�u0iu0j

vUi

vxjð8Þ

where Cε1 ¼ 1:44, Cε2 ¼ 1:92, Cm ¼ 0:09, turbulent Prandtlnumbers for k and ε are sk ¼ 1:0, and sε ¼ 1:3 respectively.

3.2. Boundary conditions and numerical method

In this study the ship motion and total resistance of shipwere simulated by RANS based code STAR-CCM þ whichenables three dimensional, VOF model simulations to capturethe free surface between air and water (Leroyer et al., 2011;Seo et al., 2012; Ozdemir et al., 2014). Similar computa-tional domain was used both ship motion and ship resistancesimulations. The general view of the computational domainwith the model hull and the notations of boundary conditionsare depicted in Fig. 2 the flow field has initially been taken as aship length at the front of the ship, two ship lengths behind theship and a ship length along the beam and depth directions,respectively.

For the numerical solution of the governing equations, thedomain is discretized in grid system (6, 254, 714), in which themesh is clustered near the hull and free surfaces. Finite volumemesh is generated entirely with unstructured hexahedral cells asshown in Fig. 3 and the total grid points are given in Table 3. At



Fig. 2. Solution domain and boundary conditions.

Fig. 3. The CAD geometry and mesh of the KVLCC2 model.

Table 3

Grid analysis.

Block Block name Grid dimension

1 Control volume 0.1921 LPP

2 Free surface 0.0960 LPP

3 Near ship 0.0192 LPP


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far field, wall with slip boundary condition is used, i.e., theentire normal velocities normal to free slip wall is zero. At shiphull, wall with no slip condition and the gradient of velocityparallel to wall is zero, as the wall shear stress is zero under freeslip condition. At the downstream boundary, zero second de-rivative for velocities in x-direction and zero gradient for freesurface is used, also a hydrostatic pressure profile is specified forthe outflow. At the symmetry plane boundaries zero derivative



condition in the normal directions are utilized. Calculations aremade in unstructured hexahedral grid computational domain forthe model hull symmetric to its centerline.

There are some works used to predict the motion and thetrajectory of moving underwater vehicles without the freesurface effects, the detailed literature can be found at Liu andPan (2014). At the velocity inlet boundary, the incident wavesare specified as the sinusoidal wave form.

The equation for surface elevation is written as:

h¼ zcosðkx� 2pfetÞ ð9ÞThe wave period T is defined as:

T¼ 1

feð10Þ

The wavelength l is defined as:

l¼ 2p

kð11Þ

The encounter wave frequency is given as:

fe ¼ffiffiffiffiffiffiffiffiffig

2pl

rþU

lð12Þ

where z is the wave amplitude, k is the wave number, U is theship speed.

The governing equations described above are discretizedusing a node based finite volume method, the advection termsare discretized using a first-order upwind interpolationscheme. The governing equations are solved successively. Thepressure field is solved by using the well-known SIMPLE al-gorithm (Patankar and Spalding, 2005). In the numericalanalysis, body attached mesh method is used to simulate theship motions.

4. Results and discussions

The main purpose of this study is to demonstrate thecapability of the general-purpose CFD solver of Star CCMþin analyzing the seakeeping characteristics by using a personalcomputer. The presented results for all cases are discretized forsingle grid and time step, based on the experience of authors'prior calculations. Due to the high computational cost, veri-fication and validation studies are not performed. All simula-tions have been carried out on an eight-parallel clustercomputer and it allows the approximating 6.5 million cells forsimulation. Some results obtained after fifteen full daysrunning on the computer are given in this section. To acquirethe added resistance, two different computations were imple-mented: a calm water resistance computation and a sea-keeping computation in head waves. Both results will bepresented discretely in the following sections.

4.1. Resistance test in calm water

The upstream flow velocity is taken as 1.044 m/s, whichgive an Fr of 0.142. The time step Dt is chosen to be 0.01 s.




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Fig. 4 shows how the resistance coefficients on hull convergetowards unsteady solution for mesh structure. The simulationsare run for a total physical flow time of 55 s, at 1.044 m/s,which corresponds to a distance of 57.4 m (approximately 10.4ship lengths). This allows sufficient time for the free surface todevelop around the hull, and permits the vessel drag force toconverge to a steady value.

Concerning the calculated results, Fig. 5 shows the wavepattern around the hull, bow and stern. The Kelvin wavepattern is very clear in this picture. The resistance test resultsare summarized in Table 4, showing comparison of the totalresistance with the experimental data. The overall agreementis very good with the experimental data and the computationsof Guo et al. (2012).

The yþ variations on the ship model for Fr ¼ 0.142 is givenin Fig. 6. The precision of yþ values on the hull determines thequality of boundary layer solution that affects the frictionforce. Moreover, it is seen that the yþ values is ranged between30 < yþ<160, as essential.

Fig. 5. Predicted wave pattern in calm water (Fr ¼ 0.142).
4.2. KVLCC2 pitching and heaving in head waves
Table 4

Comparison of the total resistance.

Experiment Present study Guo et al. (2012)

Fx (N) 18.20 19.00 18.67

Difference

��CFD�EXPEXP

�� % e 4.3% 2.60%

The seakeeping simulations of KVLCC2 was carried out asdescribed in Table 2. Three different conditions C1, C2 and C3with three different wave lengths were studied. The ship is setfree to pitch and heave motions. Time histories of the totalresistance Fx, heave motion z and pitch angle q are obtainedfrom simulations. Conditions C1, C2 and C3 have frequenciesof encounter of 0.761, 0.654 and 0.538, respectively. For thosecomputations, the similar time step value of 125 time steps perwave encounter period is used. Time histories of z and q forconditions C1, C2 and C3 are depicted in Figs. 7e9.

During the first six periods, the amplitudes of the heave andpitch motions are progressively reached its maximum values.The solutions experience a permanent response. Fig. 10 showsthe computed free surface elevations for the four-quarter periods.

The heave and pitch functions are approximated withFourier Series (FS) expansions given as (Irvine et al., 2008):

zIðtÞ ¼ zI0 þ zI1 cos�2pfetþ gz1

�þ zI2 cos�4pfetþ gz2

�þ zI3 cos

�6pfetþ gz3

� ð13Þ

qIðtÞ ¼ qI0 þ qI1 cos�2pfetþ gq1

�þ qI2 cos�4pfetþ gq2

�þ qI3 cos

�6pfetþ gq3

�ð14Þ

Fig. 4. Convergence of total drag force during computation.



where zn is the heave nth order amplitude, qn is the pitch nthorder amplitude, and gzn and gqn are the phase differences.

The amplitudes of the ship's motions is obtained by the FFTanalysis of the computed time history of ship's motion wherethe first harmonic is taken as the motion amplitude. For thisunsteady analysis, the computation time is chosen as 40 s. Inorder to diminish the effect of sampling error on the numericaladded resistance and ship motion in wave, the data in the final10 s is used for the FFT study. Numerical and experimentalFFTs of heave and pitch motions are given in Fig. 11. Nu-merical results in wave are compared with experimental datain Table 5.

The experimental results can be obtained from G2010(2010) and Guo et al. (2012). As can be seen from Table 5,the comparisons show that numerical calculations well predictthe heave and pitch motions of KVLCC2 model. FFTs of z andq mostly appearance robust response at the encounter fre-quency. The wavelength in condition C3 is very large (l/LPP ¼ 1.600) and thus displays a very linear behavior.

4.3. Added resistance

Potential flow approach is frequently used for addedresistance problems. However, for some seakeeping simula-tions, such as, green water calculations, slamming impactloading, breaking waves, etc., potential flow cannot handle theproblem properly. In order to overcome the restrictions of striptheory, efforts to extend numerical methods for viscous flows



Fig. 6. Computed yþ distributions.

Fig. 7. Computed time history of heave motion and pitch angle for C1.



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Please cite this article in press as: Ozdemir, Y.H., Barlas, B., Numerical study of ship motions and added resistance in regular incident waves of KVLCC2 model,

International Journal of Naval Architecture and Ocean Engineering (2016), http://dx.doi.org/10.1016/j.ijnaoe.2016.09.001


Fig. 10. Free surface elevation for the four-quarter periods for C1.


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have been made. The added resistance is calculated by thedifference between mean values of the total force in waves andsteady force in calm water. Steady force in calm water is givenin Table 4. Fig. 12 shows the time history of the total forces onKVLCC2 model for the conditions of C1, C2 and C3.

Added resistance calculation is based on followingequation:



Raw ¼ Raw �Rcalm ð15Þ

Raw is the mean resistance in waves and Rcalm is resistance incalm water. Added resistance coefficient Caw is obtained andnormalized according to:



Fig. 11. FFT analysis of heave motion and pitch angle.

Table 5

Amplitudes of z and q.

z (mm) q(�) fe CFD

C1 0.781

0th, 1st, EFD �6.516, 11.631 �0.137, 1.357

0th, 1st, CFD �3.375, 12.655 �0.120, 1.270

0th, 1st, Difference

��CFD�EXPEXP

�� % 48.2, 8.8 11.8, 6.3

C2 0.634

0th, 1st, CFD �4.030, 33.372 �0.977, 1.467

C3 0.537

0th, 1st, CFD �6.956, 59.333 �0.135, 2.330


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Caw ¼ Raw

rgz2B2�Lpp

ð16Þ

r is the water density, z is the wave amplitude of the incidentwaves. Fig. 13 depicts the surge forces on KVLCC2 model forC1.

The yþ variations on the ship model for the four-quarterperiods for C1 is given in Fig. 14. It is seen that the yþ

values is ranged between 30 < yþ<300, as required.As previously, stated, added resistance is defined as the

difference between the steady and 0th-order harmoniccomponent of resistance. The FFT analysis of the resistance isshown in Fig. 15 0th-order harmonic which is equal the meanvalue of resistance can be seen from the figure. First harmonic



is equal to the encounter frequency. Predicted added resis-tance in waves is compared with experimental data is given inTable 6.

A strong non-linear behavior observed in the computedforces. The comparison with the experimental measures is notwell matched for C1. The difference between predicted andexperimental value is 27.2%. Nevertheless, Guo et al. (2012)reported in their study that KVLCC2 are selected as abenchmark model in the Gothenburg 2010 CFD workshop.Five groups from four countries performed the relevantcalculation, and the seakeeping prediction for six wavelengthswas compared. The large difference near the ship motion peakarea (22.0%) reported at the Gothenburg 2010 workshop forthe wavelength l/LPP ¼ 0.9171 (C1), so it can be said that oursimulation results are not large inconsistency with other CFDsimulations.

5. Conclusions and future work

In this study, finite volume solution method for the RANSequations applied to the simulation of the KVLCC2 ship modelfor ship resistance and ship motions are studied. The mainobjective is to assess the performance of the commercial soft-ware Star CCMþ in analyzing the seakeeping characteristics ona personal computer. The standard k � ε turbulence model is



Fig. 12. Total forces on KVLCC2 model for C1, C2 and C3.

Fig. 13. Added resistance and surge force time evolution for KVLCC2 model for C1.


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used. From the simulations of the KVLCC2 ship model, thefollowing conclusions can be reached:

1. A value of calculated total resistance is satisfactory, with amargin of 4.3% to the experimental one.

2. Three different wave frequencies are studied. At low wavefrequency, there is almost a linear response to waves.

3. The results of the first harmonic and the encounter fre-quency are quite well predicted for encounter frequency of0.761.

4. The first harmonic amplitude for heave and pitch motionsshow good agreement with experimental results for



encounter frequency of 0.761. Both heave and pitch mo-tions, the peaks of the motion are good estimated. Thepoorest results occur for the 0th harmonic amplitudeswhere errors in 0th harmonic amplitudes for heave andpitch motions are 48.2% and 11.8% respectively forencounter frequency of 0.761. This may be due to theselection of the turbulence model. The use of a more so-phisticated turbulence model can modify the results. Alsostrong disagreement with the experimental data may bedue to the uncertainty involved in the experiment.

5. Present computations underestimate the added resistanceof KVLCC2 ship model for encounter frequency of 0.761.



Fig. 14. y þ variations for KVLCC2 model for the four-quarter periods for C1.

Fig. 15. FFT analysis of the resistance for C1, C2 and C3.

Table 6

Predicted added ship resistance.

CFD EFD

C1 C2 C3 C1 C2 C3

Raw (N) 52.474 63.014 33.397 e e eRaw (N) 34.474 44.014 14.397 e e e

Caw 3.349 4.403 1.440 4.601 e e


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This may indicate that the size of grid point used in thetest was not sufficient for the convergence of the addedresistance for the available computer power.

6. The largest added resistance is calculated around l/LPP ¼ 1.166. Guo et al. (2012) found similar results.

7. The wavelength in condition C3 is very large (l/LPP ¼ 1.600) and thus displays a very linear behavior.

8. A decrease in the values of yþ by means of grids couldprobably have better effects on the results.

9. The given simulations are limited to regular head waves.Likewise, the simulations can be extended to other waveconditions.

10. As expected, the finer are the grids; the better is the ac-curacy at a cost of longer computation time. Reducing thegrid size provides better representation of the bow and aftof the ship model. However, it also increases thecomputation time drastically, and sometimes the CPUmay not be able to compute the huge amount of databecause of memory deficiency. In the given simulations,the time step used depends on the encounter frequency,Dt ¼ Te/125. By using a more powerful computer, if the



grids and time step reduces, the results would probablyimprove.

11. The KVLCC2 ship model has a very complex hull profileand its motion has strongly nonlinear. The results showthat, the performance and ability of Star CCM þ forpredicting free surface flow around model ship hullgenerally appear good. Furthermore, different hull formscan be simulated for different wave lengths, wave am-plitudes, and Froude numbers.

12. Hydrodynamic parameters (added mass, added inertia anddamping ratio) can be estimated by using time series plotof ship motion study.

It was concluded that the proposed method and StarCCM þ can evaluate the ship pitch and heave motions inregular head waves accurately. In addition, added resistanceand response characteristics of motion in head waves can bepredicted in a good margin. The estimated added resistancevalues can be used to calculate the EEDI (Energy EfficiencyDesign Index) coefficient considered on ship's design stage.

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